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Science. 2016 Jul 8;353(6295):163-6. doi: 10.1126/science.aad9029.

Higher-order organization of complex networks.

Author information

1
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA.
2
Department of Computer Science, Purdue University, West Lafayette, IN 47906, USA.
3
Computer Science Department, Stanford University, Stanford, CA 94305, USA. jure@cs.stanford.edu.

Abstract

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks--at the level of small network subgraphs--remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.

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